Question

Use the probability distribution to complete parts​ (a) and​ (b) below. The number of defects per 1000 machine parts inspected Defects 0 1 2 3 4 5 Probability 0.261 0.301 0.242 0.133 0.045 0.018 ​(a) Find the​ mean, variance, and standard deviation of the probability distribution. The mean is:

Answer 1

Solution:

The formula for the mean, variance, and standard deviation for the probability distribution are given as below:

Mean = ∑ XP(X)

Variance = ∑ P(X)*(X - mean)^2

Standard deviation = Sqrt(Variance)

The calculation table is given as below:

X	P(X)	XP(X)	P(X)*(X - mean)^2
0	0.261	0	0.551784276
1	0.301	0.301	0.062040916
2	0.242	0.484	0.072144072
3	0.133	0.399	0.317885428
4	0.045	0.18	0.29169522
5	0.018	0.09	0.226334088
Total	1	1.454	1.521884

From above table, we have

Mean = 1.454

Variance = 1.521884

Standard deviation = sqrt(1.521884) = 1.233646627

Standard deviation = 1.233646627